Pith Number

pith:NTUF4IZE

pith:2012:NTUF4IZEO2KCEOV2AEAPM7HTKK

not attested not anchored not stored refs pending

Necessary conditions involving Lie brackets for impulsive optimal control problems; the commutative case

Franco Rampazzo, Maria Soledad Aronna

arxiv:1210.4532 v1 · 2012-10-16 · math.OC

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{NTUF4IZEO2KCEOV2AEAPM7HTKK}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:43:05.693426Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

6ce85e23247694223aba0100f67cf352bb3a2b8c27ea8c4fc69ec91bff69ad84

Aliases

arxiv: 1210.4532 · arxiv_version: 1210.4532v1 · doi: 10.48550/arxiv.1210.4532 · pith_short_12: NTUF4IZEO2KC · pith_short_16: NTUF4IZEO2KCEOV2 · pith_short_8: NTUF4IZE

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/NTUF4IZEO2KCEOV2AEAPM7HTKK \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 6ce85e23247694223aba0100f67cf352bb3a2b8c27ea8c4fc69ec91bff69ad84

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "25459a06fc2a13e6cb458a14d5f7314b831b4a0a7badf8e76354b9e21c0ab424",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.OC",
    "submitted_at": "2012-10-16T19:19:21Z",
    "title_canon_sha256": "90d1b991d4c525571677290c22beeac4d3ab4e82113bd3cdcd12a7bd146a8883"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.4532",
    "kind": "arxiv",
    "version": 1
  }
}